Notes on generalized special Lagrangian equation

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-05 DOI:10.1007/s00526-024-02801-w

XingChen Zhou

引用次数: 0

Abstract

We obtain a priori \(C^{1,1}\) estimates for some Hessian quotient equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The results imply the interior \(C^{2,\alpha }\) regularity for \(C^0\) viscosity solutions to \(\sigma _2=f^2(x)\) in dimension 3, with positive Lipschitz f(x).

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关于广义特殊拉格朗日方程的说明

通过研究一个扭曲的特殊拉格朗日方程，我们得到了一些具有正 Lipschitz 右边的 Hessian 商方程的 \(C^{1,1}\) 先验估计。这些结果暗示了维度 3 中具有正 Lipschitz f(x) 的 \(C^0\) 粘度解的内部 \(C^{2,\alpha }\) 正则性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.